Many types of vehicles have control systems which control a hitch or lifting apparatus to which an implement or tool is attached. With such a control system it is known to sense or determine the position of the lifting apparatus which is coupled to the vehicle, or to determine the position of implements or tools which are coupled to the lifting apparatus. Such a lifting apparatus normally includes an actuator or motor, such as hydraulic cylinders which extend between a movable linkage and an attachment frame of the vehicle. For example, front loaders have movable linkages which are a pair of rockers which are pivotably coupled to a bracket which is connected to the frame of an agricultural tractor. The movable linkage of a front loader can be coupled at its free end to the tool, for example to a shovel or to a fork. It is also known to provide front loaders of this type with sensors to determine the position of the lifting apparatus or of a tool or implement. Various control algorithms for automating the operation of the front loader, for example, for parallel guidance of the implement or in order to repeatedly or reproducibly move into an adjustable reference position, can be derived from the determined positions of the lifting apparatus or of the implements. See in this respect “Optimization possibilities for front loader work”, 58 Landtechnik January 2003, pages 26/27, “Integratable position and speed sensors for mobile hydraulics”, 59 Landtechnik April 2004, pages 206/207; “Strategies for the automated operation of front loaders”, 59 Landtechnik June 2004, page 322 et seqq., and “Operation and control strategies for automated front loader work”, 60 Landtechnik April 2005, page 230 et seqq.). The systems described in these articles are limited to the use of travel sensors, speed sensors, inclination sensors, contact sensors or to potentiometers, magneto-resistive length sensors in hydraulic cylinders, open-loop control approaches (characteristic diagram measurement of valves with referencing) as well as I/O control systems with final position switches or Hall sensors. The disadvantages of such known approaches are that, owing to their arrangement on the vehicle, the aforesaid sensors or sensor systems are frequently subjected to damage, are excessively costly or are not yet mature technology, in particular with respect to the accuracy and sensitivity of some sensors or sensor systems. For example, moving parts in the sensors or in the sensor system and the sensors or the sensor system itself often have to be protected, only achievable with large expenditure, owing to their unfavourable arrangement on the vehicle or on the lifting apparatus.
DE 199 00 587 A1 discloses an apparatus for measuring the position and angle of articulator elements of a movement system, wherein the apparatus includes acceleration sensors whose signals are employed, in an iteration method, to calculate loads and displacements of the centre of gravity on the articulator elements or on the entire movement system, in which case, after iteration has taken place, the angles and positions of the individual elements of the movement system can be calculated with respect to the vertical. The apparatus is suitable, in particular, for construction machines and forestry machines, a more detailed application of the system in such machines not being described. It is disadvantageous that the disclosed system is based on the implementation of iteration steps and therefore requires a large amount of complex computing work and in addition is inaccurate and only refers to parameter data relating to the vertical.